Best lighting for minimal shadows for product-on-white rendering
To achieve the desired result it's best to create two scenes: the first one for the product, the second for the shadow.

The first scene contains the product and all lighting like lamps, HDRI environment etc. for lighting the product as it should look like. A floor maybe for light bounces or blocking light from below the product. Set Render Properties &gt; Film &gt; Transparent. Hide the floor from the camera by disabling Object Properties &gt; Visibility &gt; Ray Visibility &gt; Camera.
Create the second scene by copying the first one (a word on linked duplicates at the end of this answer). Make the floor visible again by enabling Ray Visibility &gt; Camera and enable Visibility &gt; Ray Visibility &gt; Shadow Catcher. Delete all lamps, set World &gt; Strength to 0.0, put a plane with Emission shader above the product and play with the settings until the shadow is correct. Now hide the product from the camera like you did with the floor in the other scene.



Now both scenes are setup for rendering. In the Compositor, choose a Render Layer Node  for the shadow scene and use an Alpha Over Node with a white colour to put the shadow on a white background. Add a second Render Layer Node for the product scene and place it above the shadowed background with another Alpha Over Node.



If you hit F12 now to render the image, both scenes will be rendered and composited together.

You can now maybe save the setup as a stage for other products. If you want to change something on the product or the floor without having to create the shadow scene again it's best to make those objects linked duplicates, so any changes will apply to both of them. It's important that they're not the same objects just linked to both scenes, otherwise they cannot have different viisibility settings.
A last side note on rendering with Color Management set to Filmic: because it has a much higher dynamic range, the 'normal' white with a brightness of 1 will usually be a light grey instead of pure white. To achieve pure white in Filmic the background white must have a brightness of around 16.19 - which means, the shadow seems to disappear. Considering you want to render with Filmic it would be the best only composite the shadow and product over a transparent background and add the white in another program like Photoshop, Gimp etc.
//Edit: I've uploaded a file where I show the things described in the comments.